WASHINGTON — Governor Chris Christie of New Jersey on Sunday offered his Republican Party a prescription to win: Show up.

Christie, fresh off a 22-percentage point reelection win, said the GOP must go into Hispanic and black communities, talk with seniors, and campaign in traditionally Democratic areas. It is what helped him become the first New Jersey Republican in a quarter century to capture more than 50 percent of the vote. It also has done nothing to tamp down chatter about a 2016 presidential bid.

Christie attributed his win to reaching out to traditionally Democratic demographic groups.

‘‘Getting 51 percent of the Hispanic vote, I’m very proud of that,’’ he said. ‘‘Because I’ve worked hard with the Hispanic community to let them see how our policies can help their families. I’ve worked hard with the African-American community. I’ve worked hard with seniors and students.’’

Christie is considered a natural fit for the GOP. He’s favored an overhaul to immigration laws including a pathway to citizenship for those in the country illegally. He’s not opposed to some gun control measures. And he’s been critical of some of the Tea Party’s most popular figures in Washington.